An efficient domain decomposition method for ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

An efficient domain decomposition method for transport in porous media.
Paper
Author:Jostein R. Natvig <jrn@sintef.no> (SINTEF ICT)
Knut-Andreas Lie <knl@sintef.no> (SINTEF ICT)
Jørg Aarnes <jaa@sintef.no> (SINTEF ICT)
Presenter:Jostein R. Natvig <jrn@sintef.no> (SINTEF ICT)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000457
DOI:10.4122/1.1000000458

Convection dominated transport of fluids in a porous media is governed by a nonlinear equation. Explicit time discretisations of this equation are subject to a very restrictive stability condition on the time step, due to variable background velocity and porosity fields. It is therefore common to resort to implicit time discretisation. This results in better stability, but one has to solve large systems of nonlinear equations for each time step. We present an efficient solver for hyperbolic transport equations with positive characteristics. Our solver is based on an implicit discretisation combined with overlapping domain decomposition. By applying an optimal ordering algorithm for each subdomain, the discrete system of nonlinear equations can be solved in one grid block at a time. This way, we avoid assembly in each subdomain of a full nonlinear system. Our approach allows us to handle large numbers of grid blocks with modest requirements on memory. Physical terms violating our assumptions of positive characteristics (e.g., gravity and capillary forces) can be treated by a standard operator splitting.